Question

Which number is a solution of $\frac{x}{-7}<6$?

1. $-100$
2. $-56$
3. $-42$
4. $-14$

Short answer

The correct option is (a) & (b).

Step-by-step solution

Step -1 - Apply the concept of linear equations

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Sideto maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the value of x

Here, the inequality is $\frac{x}{-7}<6$

To solve this, simply multiply $-7$to both side of the equation

$\begin{array}{l}\frac{x}{-7}<6\\ \frac{x}{-7}\times -7<6\times -7\\ x<-42\end{array}$

Step -3 – Eliminating the options to get correct one

a. $-100$:This is a correct option because the value of solution is smaller than $-42$and$-100$ is smaller than $-42$.

b. $-56$: This is a correct option because the value of solution is smaller than $-42$ and $-56$ is smaller than $-42$.

c. $-42$: This is not a correct option because the value of solution is smaller than $-42$

but $-42$ is not equal to the given solution.

d. $-14$: This is not a correct option because the value of solution is smaller than $-42$ but $-14$ is greater than $-42$.